Design Briefs: Equations for determining common-mode performance

Using Equation 2 (below) with Excel can be a useful tool in determining a range of possible CMRR values given a resistor tolerance. First, generate a set of random numbers with a normal distribution based on the tolerance you intend to use in the design (mean = 0.0, and standard deviation = 0.04—for a 0.1% resistor 2 x 1 % / 5 Σ). Use this random number as a factor to generate a set of resistance values that are adjusted for tolerance. The resistance values are applied to Equation 2 to generate a distribution of common-mode outputs that varies according to the tolerance of the resistors.

Equation 2: Differential Output Using Unique Resistor Values:

The figure shows distributions generated for 0.1% resistors using this technique.

A prototype of this circuit was used to verify that CMR fell within the predicted distribution. Note that the CMR could be dramatically improved using a trim potentiometer in series with R1. The prototype circuit's CMR was adjusted to greater then 100 dB through trimming.

The maximum common-mode input occurs when the voltage at the THS4130's inputs exceeds the maximum common-mode input voltage range. The relationship for this voltage was derived through nodal analysis (Equation 3, below). Applying the values shown in Figure 1 predicts that the voltage at node "w" will be V_w = 4.5 V with a 90-V common-mode signal. This is the specified maximum common-mode input voltage for the THS4130. Empirical measurements verify that the circuit's maximum common-mode input is 90 V.

Equation 3: